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Area
Area is a measure of how much space is inside a shape. Think of it like a big carpet that you can lay down on the floor. The bigger the carpet, the more space it takes up.
Just like a carpet, different shapes have different areas. A square carpet takes up more space than a round one, and a rectangular carpet takes up more space than a triangle one.
A way to measure the area of a shape is to count the number of little squares that fit inside it. For example, if you have a square that is made up of 10 little squares, its area is 10 square units.
Another way to measure the area of a shape is to multiply the length and width of the shape together. For example, if a rectangle is 3 units long and 4 units wide, its area is 3 x 4 = 12 square units.
So, to sum up, area is a way to measure how much space is inside a shape and it's measured in square units like square feet, square meters, square inches.
Area of various common shapes
Square:
- Formula: Area = side^2
Rectangle:
- Formula: Area = length × width
Triangle:
- Formula: Area = (base × height) / 2
Circle:
- Formula: Area = π × radius^2
Parallelogram:
- Formula: Area = base × height
Trapezoid:
- Formula: Area = ((base1 + base2) × height) / 2
Rhombus:
- Formula: Area = (diagonal1 × diagonal2) / 2
Pentagon:
- Formula: Area = (side^2 × sqrt(25 + 10 × sqrt(5))) / 4
Hexagon:
- Formula: Area = (3 × sqrt(3) × side^2) / 2
Octagon:
- Formula: Area = 2 × (1 + sqrt(2)) × side^2
Ellipse:
- Formula: Area = π × a × b
Annulus:
- Formula: Area = π × (outer radius^2 - inner radius^2)
Sector of a Circle:
- Formula: Area = (θ/360) × π × radius^2
Equilateral Triangle:
- Formula: Area = (sqrt(3) × side^2) / 4
Isosceles Triangle:
- Formula: Area = (base × height) / 2
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